Most measurements of fluid mixing and fluid(s) flow(s) are direct. One or more fluid flows may simply be measured while such flows are occurring. Alternatively, any mixture that results from the flows of two or more fluids may be analyzed as to its constituent components in order to quantitatively determine the fluid flows that have transpired.
However, direct measurement of fluid(s) flow(s), such as within the blood stream of a living animal, is often impossible. Meanwhile, direct quantitative analysis of the constituent components of complex, or extensive, mixtures of fluids is often prohibitively difficult or expensive. The expense is magnified if many samples must be taken, and analyzed, over time.
Accordingly, modeling or simulation is sometimes used in order to trace the flow, and mixing, of one or more fluids. For example, a dye may be put in ground water and its dispersion may subsequently be observed. From the observed dispersion of the dye a similar dispersion or pollutants, or other less readily detectable fluids, may be imputed.
Another, sophisticated, form of fluid flow and fluid mixing analysis is indirect. A physical marker is put into, or a chemical marker is bonded to, an actual fluid, or fluid component, for which flow and/or mixing is desired to be assessed. The fluid serves as a carrier. When the distribution of the marker is analyzed then the corresponding distribution of the carrier fluid is imputed.
The highest, and most exacting, expression of this indirect method is in medicine, and particularly in blood flow analysis. The blood, and the organs and tissues receiving blood, within a living animal present a system that is very complex in its fluid flow patterns and dynamics, and that is difficult of direct access and measurement. Accordingly, microscopic markers are placed in the animal's blood where they are subsequently distributed to the animal's tissues. The tissues are subsequently harvested, and the prevalence--i.e., the numbers--of the markers are analyzed, producing thereby an indirect indication of the blood flow to the tissue.
Previous systems that have been developed for medical blood flow analysis--discussed in greater detail hereafter--have proven to be both complex and expensive. Because of their cost and complexity, such systems have not been found suitable for use in routine industrial or environmental fluid flow and mixing measurement problems.
However, it should be recognized that the flow of blood, or blood components, within the arteries and veins of a living animal is only different in complexity, and not in the essential nature of fluid flow dynamics, from the flows of fluids occurring within factories, ecosystems, and the like. Accordingly, if a reliable, effective, and inexpensive indirect fluid flow measurement system suitable for use on the difficult problem of blood flow analysis could be developed, then such a system might well have general applicability to the tracing and measurement of fluid flows, and the mixing of fluids, in diverse environments.
2.1 The Measurement of Blood Flow
The reasons for the measurement of blood flow are set forth in U.S. Pat. No. 4,616,658, discussed in greater detail in following section 2.2. The following discussion is adopted from the discussion within that patent.
The measurement of blood flow in experimental animals is often necessary in the fields of pharmacology, physiology, therapeutics and diagnostics. For example, toxicology studies require blood flow measurement to determine the toxicity of various suspected toxic agents. Further, many diagnostic and therapeutic advances have some impact on the flow of blood. It is therefore desirable to take blood flow measurements.
Blood flow measurements can be performed in many anatomical areas, including the brain, heart, lung, gut, kidney, reproductive organs, skin and muscle. One sensitive and specific previous technique involves the use of radioactively labeled microspheres. In one variant of the technique plastic microspheres are marked with a radioactive label and injected into the left atrium of the heart of an experimental animal. The spheres disperse in proportion to blood flow and lodge in the tissue in direct proportion to the blood flow to that tissue. The animal is then sacrificed and the organ(s) of interest is (are) harvested. Blood flow to a particular organ is determined by measuring the level of radioactivity in the organ, which radioactivity is a function of the number of spheres trapped in the organ's capillaries.
Although the use of radioactively labeled microspheres is sensitive and specific, there are several problems and disadvantages associated with the method. First, startup costs are very high, as they include purchase of a gamma counter to measure radioactivity, lead shielding to protect laboratory workers from radiation exposure, complex storage facilities and a high minimum "per order" cost of equipments from manufacturers. These high costs severely limit the availability of this type of blood measurement, generally restricting its use to large laboratories and medical centers.
Second, up to ten successive measurements per animal can be made using radioactively labeled microspheres, due to the overlap between the emission energies of available radiolabels. Moreover, the measurement of even five blood flow stages requires the use of a complex computer program to analyze and separate the data obtained, further limiting the availability of the technique.
Third, radiolabeled microspheres have a limited shelf life, ranging from one week to several months. Even where the shelf life is at the high end of this range, the continuous decay makes continual recalibration of the testing apparatus necessary.
Fourth, laboratory workers using radioactive microspheres are exposed to substantial radiation danger because many of the isotopes used as labels emit high levels of energy. Accordingly, the costs, and risks, involved in minimizing radiation exposure are substantial.
Finally, and perhaps most critically, disposal of the experimental animals poses significant problems, ecologically, logistically and financially. Because the entire animal carcass remains radioactive for several years after disposal, it must be placed in a special low level radiation dump, to which dumps there is increasing public antipathy. The cost of disposal is becoming prohibitively high, recently ranging to as high as $550 U.S. per animal.
2.3 Particular Previous Methods of Blood Flow Measurement
In 1967, plastic, radioactively labelled microspheres (RM) were introduced for the measurement of regional perfusion. See Rudolph A. M. , Heymann M. A.: The circulation of the fetus in utero: Methods for studying distribution of blood flow, cardiac output and organ blood flow. Circ Res 1967;21:163-184.
One year later, Makowski et al introduced a blood withdrawal technique for the quantification of regional blood flow. See Makowski E. L., Meschia G., Droegemueller W., Battaglia F. C.: Measurement of umbilical arterial blood flow to the sheep placenta and fetus in utero: Distribution to cotyledons and the intercotyledonary chorion. Circ Res 1968;23:623-631.
In 1969, Domenech et al first validated the use of radioactive microspheres (RM) for the measurement of regional myocardial blood flow (RMBF). See Domenech R. F., Hoffman J. I. E., Noble M. I. M., Saunders K. B., Henson J. R., Subijantos: Total and regional coronary blood flow measured by radioactive microspheres in conscious and anesthetized dogs. Circ Res 1969;25:581-596. Thereafter, this method has become the standard technique for the measurement of RMBF in various experimental settings. However, due to the precautionary measures needed to minimize radiation exposure, use of RM is restricted to specially licensed laboratories. Storage of the radioactive microspheres, as well as disposal of radioactive waste, is expensive and an environmental hazard.
To avoid some of these limitations inherent to the RM method, U.S. Pat. No. 4,616,658 to Shell et al for NON-RADIOACTIVELY LABELED MICROSPHERES AND USE OF SAME TO MEASURE BLOOD FLOW describes a method for measuring RMBF using non-radioactive, colored microspheres (CM). Later, Hale et al describe a similar technique. See Hale S. L., Alker K. J., Kloner R. A.: Evaluation of nonradioactive, colored microspheres for measurement of regional myocardial blood flow in dogs. Circulation 1988;78:428-434.
According to the techniques of Shell et al and Hale et al, microspheres may be labeled with colored dyes, and subsequently visually identified and counted in tissue, either after separation therefrom or while still trapped in the tissue's capillaries. Shell et al also describe labeling microspheres by linkage to enzymes, particularly plant enzymes, and, after extraction from tissue, measuring the density of enzyme-linked spheres by a measurement of optical density which is indicative of enzyme activity.
In the previous techniques using non-radioactively labeled colored microspheres (CM), tissue samples that have captured microspheres from the circulating blood of a live animal are surgically harvested and are then digested by a combination of enzymatic and chemical methods. Aliquots of the microspheres trapped within a given sample are then counted in a hemacytometer by an investigator using light microscopy, or, in the case of enzyme-linked microspheres, by measurement of optical density to determine enzyme activity.
There are, however, significant limitations to these previous techniques. First, RMBF is extrapolated from only a small aliquot of the colored microspheres (CM) actually trapped within the sample, thereby entailing a substantial statistical error in RMBF calculations. Second, the use of only three different colors has been validated, and then in only a small number of samples, whereas it is clearly desirable to be able to make more than three measurements of RMBF in many experimental protocols. Third, there is a considerable variation in the diameter of the CM used in previous studies, as admitted by Hale et al. Fourth, the prior methods require substantial time for the tedious counting of individual colored microspheres. Fifth, in preliminary experiments, the inventors of the present invention found it almost impossible to distinguish visually the nine (9) commercially available microsphere colors in the reddish background of digested myocardium.
Recently, still another alternative non-radioactive method for measuring RMBF was developed by Morita et al using X-ray fluorescence excitation of microspheres loaded with elements of high atomic number. See Morita Y., Payne B. D., Aldea G. S., McWattes C., Huseini W., Mori H., Hoffman J. I. E., Kaufmann L.: Local blood flow measured by fluorescence excitation of nonradioactive microspheres. Am J Physiol 1990;258:H1573-H1584. So far, only two different labels have been reported to have been validated by comparison to RM after intracoronary injection in two dogs. The method of Morita et al could be hampered by leaching of the label from the microspheres over time. Another disadvantage is the need of a sophisticated and relatively expensive equipment for X-ray excitation and fluorescence detection which is not commercially available.
The previous blood flow analysis methods employing colored microspheres, including the method of Morita et al, require that the numbers of microspheres per unit portion of a recovered tissue sample should be determined. Because the numbers of microspheres introduced within the blood, and captured within the capillaries of the tissue, are enormous, and on the order of 10.sup.6, the actual numbers are commonly only estimated by statistical sampling, which induces measurement error. Worse, even the determination of the numbers of colored microspheres that are within minute samples is tedious and expensive, involving in the methods of Shell et al and of Hale et al manual observations through a microscope.
In order to circumvent these limitations, it would be desirable if a new method of producing and/or using microspheres, and of measuring RMBF therewith, could support both (i) easy tissue processing and (ii) quantitative, automated, and easy counting of all the microspheres within an individual sample. Such a new method would desirably be both economical and validated by a rigorous comparison to RM over a range of RMBF from 0 to 10 ml/(min g) on many hundreds, or thousands, of individual myocardial samples. If such a method were to be suitably economical, reliable, easy to use, and devoid of significant drawbacks, then it might find general use in the measurement and analysis of diverse fluid flow and fluid mixing problems other than only medical problems.